| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Identify errors in student work |
| Difficulty | Moderate -0.3 This is a slightly easier than average A-level question. Part (a) requires spotting a common logarithm error (incorrect application of log subtraction rule), which is straightforward pattern recognition. Part (b) involves standard logarithm manipulation, solving a quadratic, and checking validity of solutions—all routine AS-level techniques with no novel problem-solving required. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| The student goes wrong in line 2, where the subtraction should be a division as \(\log x - \log y = \log\frac{x}{y}\) | B1 | (1 mark) |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = 6, x = 3\) | M1, M1, A1 | Using the subtraction law and power law correctly; Student obtains a quadratic and correctly factorises their quadratic; Both values of \(x\) are correct |
### Part a:
The student goes wrong in line 2, where the subtraction should be a division as $\log x - \log y = \log\frac{x}{y}$ | B1 | (1 mark)
### Part b:
$x = 6, x = 3$ | M1, M1, A1 | Using the subtraction law and power law correctly; Student obtains a quadratic and correctly factorises their quadratic; Both values of $x$ are correctA student is asked to solve the equation
$$\log_3 x - \log_3 \sqrt{x - 2} = 1$$
The student's attempt is shown
$$\log_3 x - \log_3 \sqrt{x - 2} = 1$$
$$x - \sqrt{x - 2} = 3^1$$
$$x - 3 = \sqrt{x - 2}$$
$$(x - 3)^2 = x - 2$$
$$x^2 - 7x + 11 = 0$$
$$x = \frac{7 + \sqrt{5}}{2} \text{ or } x = \frac{7 - \sqrt{5}}{2}$$
\begin{enumerate}[label=(\alph*)]
\item Identify the error made by this student, giving a brief explanation. [1]
\item Write out the correct solution. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q5 [4]}}